What is dm/dt and the meaning of d and how this equation is used in respect to conservation of momentum
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In words, the net force acting on an object causes its momentum to change. If the net force is zero, the momentum does not change, it is conserved. d(mv)/dt = v dm/dt + m dv/dt = v dm/dt + m a. If the mass of the object is constant, dm/dt = 0 so d(mv)/dt = m a and the two versions of Newton's second law are equivalent.
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dm/dt is used in situations with variable mass. for example: when a rocket goes up, it consumes its fuel and hence looses mass or there is a chnge in mass (from the initial mass)...When mass is variable, F(force)=d(mv)/dt. This can be also written as F= m.(dv/dt) + v.(dm/dt).
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